Abstract:
In this paper we consider the econometric analysis of exponential-affine term-structure models using a panel-data approach. As we assume that all zero-coupon yields are observed with measurement error, we take the state variables as unobserved and use the Kalman filter to estimate the model parameters. For Gaussian models, this approach provides the exact likelihood function, but the main focus of the paper is on non-Gaussian, exponential-affine models. Since the exact filter and likelihood function are unknown, the suggestion in the literature is to use a QML estimator obtained from the first and second conditional moments of the state variables. However, this QML estimator is not consistent.

Latest revision: November 1997.

Abstract:
The state space form is a useful framework for estimating Markovian term-structure models with unobserved state variables. In this paper, we consider an econometric method which accomodates non-linearity in the measurement equation, for example when estimating exponential-affine models using prices of coupon bonds. The filtering algorithm is known as the iterative, extended Kalman filter (IEKF), and the model parameters are estimated by quasi maximum likelihood (QML), based on predictions errors obtained from the IEKF recursions. While, in general, the QML estimator is inconsistent, a Monte Carlo study demonstrates that the biases are very small, and economically insignificant, in sample configurations that are representative of real-world data.

The main contribution of the paper is a detailed account of an efficient computer implementation of the QML-IEKF technique. In this process, we calculate general expressions for the analytical derivatives of the log-likelihood function and the IEKF recursions, including the update step which is only defined implicitly as the solution to a non-linear GLS problem.

Latest revision: June 1997.